second-order
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21: 3.7 Ordinary Differential Equations
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►Consideration will be limited to ordinary linear second-order
differential equations
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Second-Order Equations
…22: 1.13 Differential Equations
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►A standard form for second order ordinary differential equations with , and with a real parameter , and real valued functions and , with and positive, is
…This is the Sturm-Liouville form of a second order differential equation, where ′ denotes .
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23: 16.14 Partial Differential Equations
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►In addition to the four Appell functions there are other sums of double series that cannot be expressed as a product of two functions, and which satisfy pairs of linear partial differential equations of the second order.
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24: Bibliography B
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Uniform asymptotic solutions of a class of second-order linear differential equations having a turning point and a regular singularity, with an application to Legendre functions.
SIAM J. Math. Anal. 17 (2), pp. 422–450.
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Asymptotic Expansions for the Coefficient Functions Associated with Linear Second-order Differential Equations: The Simple Pole Case.
In Asymptotic and Computational Analysis (Winnipeg, MB, 1989), R. Wong (Ed.),
Lecture Notes in Pure and Applied Mathematics, Vol. 124, pp. 53–73.
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25: Bibliography M
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On the choice of standard solutions for a homogeneous linear differential equation of the second order.
Quart. J. Mech. Appl. Math. 3 (2), pp. 225–235.
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Hyperasymptotic solutions of second-order ordinary differential equations with a singularity of arbitrary integer rank.
Methods Appl. Anal. 4 (3), pp. 250–260.
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26: Bibliography S
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Liouville-Green approximations for a class of linear oscillatory difference equations of the second order.
J. Comput. Appl. Math. 41 (1-2), pp. 105–116.
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A Survey on the Liouville-Green (WKB) Approximation for Linear Difference Equations of the Second Order.
In Advances in Difference Equations (Veszprém, 1995), S. Elaydi, I. Győri, and G. Ladas (Eds.),
pp. 567–577.
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27: DLMF Project News
error generating summary28: Bibliography K
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An algorithm for solving second order linear homogeneous differential equations.
J. Symbolic Comput. 2 (1), pp. 3–43.
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29: 3.6 Linear Difference Equations
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►Many special functions satisfy second-order recurrence relations, or difference equations, of the form
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